Scaling Up (Part 1)

Key Concepts

• Distributed Training: Training machine learning models across multiple accelerators (GPUs, TPUs) to handle large models and datasets.
• SPMD (Single Program Multiple Data): Jax's paradigm where a single program is written and compiled to run efficiently across multiple physical devices.
• Distributed Data Parallelism (DDP): Replicating the model on each device, splitting data batches, and averaging gradients for synchronization.
• Fully Sharded Data Parallelism (FSDP): A memory-efficient variant of DDP that shards parameters, gradients, and optimizer states across devices.
• Tensor Parallelism (Model Parallelism): Splitting computations within a single large layer across multiple devices.
• Mesh: A logical arrangement of physical hardware (e.g., a grid) used to define how tensors are distributed.
• Partition Spec (P): A tuple defining how tensor dimensions are sharded or replicated across mesh axes.
• Named Sharding: An object combining a mesh and a partition spec to define tensor distribution.
• jax.device_put: A function to move data to accelerators and arrange it into specified shards.
• jax.jit: Jax's just-in-time compilation decorator that enables automatic parallelization and optimization.
• jax.lax.with_sharding_constraint: A function to enforce specific sharding for intermediate computation results within a jax.jit compiled function.
• Flax NNX: A framework for building neural networks in Jax, integrating with its distributed computing capabilities.

Distributed Training: The Need and Jax's Approach

The primary motivation for distributed training stems from the immense scale of modern machine learning models and datasets. Multi-billion parameter models are often too large to fit onto a single accelerator. Distributed training addresses this by breaking down the computational problem. Jax employs the SPMD (Single Program Multiple Data) paradigm, where developers write code as if for a single, large logical device, and the Jax compiler optimizes its execution across numerous physical devices.

Styles of Parallelism

Distributed Data Parallelism (DDP)

DDP is a fundamental approach to speed up training by parallelizing data processing.

• Process:
  1. The model is replicated identically onto each accelerator (GPU/TPU).
  2. The data batch is split among these devices.
  3. Each device processes its unique data slice in parallel, computing local gradients.
  4. These local gradients are then averaged across all devices.
  5. This single, averaged gradient is used to update all model copies identically, ensuring synchronization.
• Benefit: Significantly reduces overall training time by processing data in parallel.
• Limitation: Replicates the entire model state on each device, consuming substantial GPU/TPU memory.

Fully Sharded Data Parallelism (FSDP)

FSDP enhances DDP by being highly memory-efficient.

• Process:
  1. It remains a form of data parallelism, with different data per device.
  2. Crucially, FSDP shards parameters, gradients, and optimizer states across all devices.
  3. Each device only stores its assigned slice of these components.
  4. Full parameters for a layer are temporarily gathered only when computation is required and then the memory is freed.
• Benefit: Drastically reduces memory usage per device, enabling larger models or batch sizes on the same hardware compared to standard DDP.

Tensor Parallelism (Model Parallelism)

Tensor parallelism addresses scenarios where a single model layer is too large for one accelerator.

• Process: Instead of splitting data, it splits the computations within a massive layer across multiple devices. This is analogous to multiple machines collaborating on a single large matrix multiplication, each performing a portion of the calculations on the same data.
• Benefit: Allows running models with extremely large layers that exceed individual GPU/TPU memory capacity.
• Requirement: Demands fast communication between devices.

Jax Primitives for Explicit Parallelism

Jax provides core primitives for implementing explicit parallelism:

The Mesh

• Concept: A mesh represents a logical arrangement, often a grid, of the physical hardware. Axes of this grid are typically named.
• Example: A common setup is a 2D mesh with data and model axes. The data axis often refers to devices used for data parallelism, and the model axis for model parallelism.
• Function: The mesh object serves as a reference for how tensors will be distributed.
• Code Example: A mesh can be created for eight devices in a 4x2 grid, potentially for a V28 TPU.

Partition Spec (P)

• Concept: Partition spec, imported as P, defines how a specific tensor (e.g., a weight matrix, input batch) is laid out across the mesh. It's a tuple where each element corresponds to a tensor dimension.
• Usage:
  • An element can be the name of a mesh axis to shard along that dimension.
  • An element can be None to replicate the tensor along that axis.
  • An empty P signifies that the tensor is fully replicated everywhere.
• Code Examples: Illustrate sharding and replication across data and model mesh axes.

Named Sharding

• Concept: A named sharding object combines a mesh and a partition spec, providing a complete definition of how a tensor should be distributed.

jax.device_put

• Function: This is the key function to apply sharding. It takes data (often starting as a NumPy array) and a named sharding object.
• Action: Jax handles moving the data to the accelerators and arranging it into the specified shards according to the named sharding.
• Application: Crucial for preparing input batches for distributed training.
• Code Example: Demonstrates creating a named sharding and using jax.device_put to distribute shards.

jax.jit and SPMD Magic

• Mechanism: The SPMD paradigm's power is largely realized within jax.jit.
• Process: When a function is decorated with jax.jit and receives sharded arrays (like those produced by jax.device_put), the XLA compiler analyzes the operations and input shardings.
• Outcome: The compiler automatically parallelizes the computation, determining which parts run on which devices and inserting necessary communication operations (e.g., all_reduce for gradient aggregation).

jax.lax.with_sharding_constraint

• Purpose: Provides more control within a jax.jit compiled function.
• Function: Allows developers to explicitly tell the compiler to ensure an intermediate result adheres to a specific sharding.
• Use Cases: Useful for performance tuning and ensuring computational correctness.

Looking Ahead: Integrating Jax with Flax NNX

The next episode will focus on bridging Jax's functional programming style with Flax NNX's object-oriented approach. Key topics will include:

• Embedding sharding instructions directly into neural network definitions within NNX.
• Safely initializing large, sharded models within a jax.jit compiled function to avoid out-of-memory errors on single accelerators.

Conclusion

This episode introduced the fundamental concepts of distributed training, highlighting the necessity driven by model and data scale. It detailed Jax's SPMD paradigm and the core primitives: mesh, partition spec, and jax.jit. These tools enable the description of hardware layouts and data arrangements. The discussion also touched upon DDP and the memory-efficient FSDP, as well as tensor parallelism for handling large layers. The foundation is now laid for understanding how to apply these Jax primitives to stateful Flax NNX models in subsequent episodes.